Isoperimetric functions of groups, connections between group theory,topology and computer science

Mark Sapir of Vanderbilt University

One of the main results says that the function $f(l)=l^a$, $a>4$, is (O-equivalent to) the isoperimetric function of a group if and only if $a$ is a relatively fast computable number. For example, there exists a manifold with isoperimetric function equivalent to l^(\pi+e). We also construct the first example of an NP-complete group, and characterize the groups with word problem in NP: a finitely generated group has word problem in NP if and only if it is a subgroup of a finitely presented group with polynomial isoperimetric function.

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The paper involved, the Annals of Math. (157,2002) can be obtained at www.math.vanderbilt.edu/~msapir/publications.html"